Question

Solve ${\left(\sqrt[3]{3\frac{2}{3}}\right)}^{x-1}=\frac{27}{8}$

Answer 1

${\left(\sqrt[3]{3\frac{2}{3}}\right)}^{x-1}=\frac{27}{8}$

${\left(\frac{2}{3}\right)}^{\frac{x-1}{3}}={\left(\frac{3}{2}\right)}^3$

${\left(\frac{2}{3}\right)}^{\frac{x-1}{3}}={\left(\frac{2}{3}\right)}^{-3}$

$\frac{x-1}{3}=-3$

$x-1=-9\Rightarrow x=-8$